Some protesters sprayed graffiti on cars and buildings and destroyed shop windows, local media in Portland reported.

"Many in the crowd are trying to get anarchist groups to stop destroying property, anarchists refusing. Others encouraged to leave area," the department said on Twitter after declaring the demonstration a riot.

Portland has witnessed some of the most violent anti-Trump protests so far [Steve Dipaola/Reuters]

As thousands of people marched, some vandalised shop windows, lit firecrackers and set waste bins on fire.

An estimated 4,000 protesters chanted "We reject the president-elect!", with some throwing objects at police, prompting several arrests.

On the East Coast, protests occurred in Washington DC, Baltimore, Philadelphia and New York, while on the West Coast demonstrators rallied in Los Angeles, San Francisco and Oakland in California besides Portland.

Dozens in Minneapolis marched on to Interstate 94, blocking traffic in both directions for at least an hour as police stood by.

Teenagers and young adults tend to dominate the racially mixed crowds [Steve Dipaola/Reuters]

A smaller band of demonstrators briefly halted traffic on a busy Los Angeles freeway before police cleared them off.

Baltimore police reported that about 600 people marched through the downtown Inner Harbor area, with some blocking roadways by sitting in the street.

Two people were arrested, police said.

Shop windows and cars have been vandalised and dumpsters set on fire [Steve Dipaola/Reuters]

In Denver, a crowd that media estimated to number about 3,000 gathered on the grounds of the Colorado state capitol and marched through downtown in one of the largest of Thursday's events.

Hundreds also demonstrated in Dallas.

Thursday's gatherings were generally smaller in scale and less intense than Wednesday's, and teenagers and young adults again dominated the racially mixed crowds.

"Just had a very open and successful presidential election. Now professional protesters, incited by the media, are protesting. Very unfair!" Trump said in on Twitter on Thursday night.

Police pitched special security barricades around two Trump marquee properties that have become focal points of the protests - his newly opened Pennsylvania Avenue Hotel in Washington DC and Trump Tower, where he lives in Manhattan.

Protesters have been accused by Trump of not respecting the democratic process [Steve Dipaola/Reuters]

In the nation's capital, about 100 protesters marched from the White House, where Trump had his first transition meeting with President Barack Obama on Thursday, to the Trump International Hotel several blocks away.

At least 200 people rallied there after dark, many of them chanting "No hate! No fear! Immigrants are welcome here!" and carrying signs with such slogans as "Impeach Trump" and "Not my president".

Trump supporters say the protesters are not respecting the democratic process.

As of Thursday, Hillary Clinton, the Democratic Party candidate, was leading Trump in votes nationwide 47.7 percent to 47.5 percent, but Trump secured victory in the Electoral College.